CBSE Class 12-science Answered

Solve for x : 2 tan?1 (cos x) = tan?1 (2 cosec x).

Asked by ambigamagendran256 | 04 Nov, 2023, 05:43: AM

Expert Answer

Let us consider

begin mathsize 14px style space 2 space tan to the power of negative 1 to the power of space end exponent left parenthesis cos x space right parenthesis space equals space tan to the power of negative 1 end exponent left parenthesis 2 space cos e c x space right parenthesis space equals space alpha end style

From LHS , we get

begin mathsize 14px style tan to the power of negative 1 end exponent left parenthesis cos x right parenthesis space equals space alpha over 2 end style

begin mathsize 14px style tan space alpha over 2 space equals space cos x end style

.............................. (1)

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From RHS , we get

begin mathsize 14px style tan space alpha space equals space 2 space cos e c space x end style

Above expression is written as

begin mathsize 14px style fraction numerator 2 space tan begin display style alpha over 2 end style over denominator 1 space minus space tan squared begin display style alpha over 2 end style end fraction space equals space fraction numerator 2 over denominator sin x end fraction space end style

By substituting tan(α/2) from eqn.(1) , above expression is written as

begin mathsize 14px style fraction numerator 2 space cos x over denominator 1 space minus space cos squared x end fraction space equals space fraction numerator 2 over denominator sin space x end fraction end style

begin mathsize 14px style fraction numerator 2 space cos x over denominator sin squared x end fraction space equals space fraction numerator 2 over denominator sin space x end fraction end style

From above , we get

begin mathsize 14px style sin space x space equals space cos space x end style

or x = π/4

Answered by Thiyagarajan K | 04 Nov, 2023, 08:05: AM

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